I don't think you're far off the mark at all. Songs get offered to band's all the time and that how Def Leppard ended up recording Long Long Way To Go from their X album in 2002 (also written by Wayne Hector). Def Leppard didn't take any writing credits on that one though. I think after She Don't Know Me Jon refuses to record a song that he isn't credited on. Maybe he changed a line here or there just to get it on there. But yeah, I don't think he sat down and write this with them at all. I think it was sent to him and he maybe tweaked it a little.